Minkowski versus Euclidean rank for products of metric spaces.
Foertsch, Thomas, Schroeder, Viktor (2002)
Advances in Geometry
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Displaying similar documents to “Isometric Embeddings of Pro-Euclidean Spaces”
Minkowski versus Euclidean rank for products of metric spaces.
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In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.
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Linearly rigid metric spaces and the embedding problem
J. Melleray, F. V. Petrov, A. M. Vershik (2008)
Fundamenta Mathematicae
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We consider the problem of isometric embedding of metric spaces into Banach spaces, and introduce and study the remarkable class of so-called linearly rigid metric spaces: these are the spaces that admit a unique, up to isometry, linearly dense isometric embedding into a Banach space. The first nontrivial example of such a space was given by R. Holmes; he proved that the universal Urysohn space has this property. We give a criterion of linear rigidity of a metric space, which allows...